While n-dimensionalQuake, in theory, would be an extremely interesting thing, the fact of the matter is that not everyone gets the same thrill out of watching several bots destroy each other in new and interesting ways. The true problem lies at the heart of the matter: expanding the bot-match to include the ever-limited perspective of the actual Quake player.

It took me a few seconds to get used to thinking in two dimensions, back when Wolfenstein 3D was released. The Doom series introduced an entirely new challenge: psuedo-3D gaming. This tiny shift took a couple of hours to understand, and I found myself reeling at the concept of how hard it would be to actually play a game where vertical aiming was not handled by the computer.

Unfortunately, I saw the enemy and it was Quake. I spent days trying to understand the concept of actually thinking, moving, looking, and aiming in three dimensions. I spent months working on coordinating the efforts of the hand I kept on the keyboard with the hand I used to move the devilish mouse. Even after a few years, I'm still struggling to cope with what has become a staple in the first person shooter community.

My point is that even if you could strap a volunteer into a rig that is designed for n-dimensional movement, from conventional compass directions with the left hand to twelfth dimension, uh, movements with an optical sensor designed to pick up the miniscule flaring motions of the nostrils, there are very few humans on earth that would have the sheer will and mental capabilities required to grasp both the physics of the game and comprehend the controls. While it would be interesting to think that opening and closing your jaw could extend your digital self into dimensions normally only seriously discussed on Star Trek, the fact that sneezing could inadvertantly land your player in ancient Greece would tend to put a damper on your search for the enemy flag.

Clearly the display of that "extra" dimensional information is the problem. To remedy this the level will be a true 4-d hyperspace (w,x,y,z) but at any time t the quake 3 map will be a "slice" of that 4-d hyperspace as it intersects a 3-d space.

This is much like showing a sphere to a flatlander by pusing it through her flat 2-d universe. It would first appear as a point, then as a circle growing in size, then shrinking, and finally disappearing altogether. Now just extend that analogy up a dimension. You'll have a quake 3 map that confusingly changes shape as time progresses. It even presents the possibility that a player could become "trapped" in an area of the map that is shrinking out of existence.

Mathematically it is quite feasible. Anyone who has taken a good multivariable calculus course knows (or knew) all of the basics necessary for moving an action game from 2 dimensions to 3, 4, or 17. It's certainly harder math, but not to the extent that it would be an obstacle. And since bots are essentially avatars controlled by real-time calculations involving the surrounding environment, controlling bots shouldn't be a problem either.

The problem would come with the human element. Creating artwork for the game that is meaningful in more than three dimensions might be tricky; how do you sculpt an n-dimensional model for a bot player if you don't even know how an n-dimensional human being ought to look? Assuming that problem can be circumvented (as well as the headache of designing aesthetically pleasing n-dimensional maps), the only real problem would be displaying the action on the screen in a comprehensible manner. As scienceman points out, the map would have the disconcerting behavior of pulsating and changing as your three-dimensional cross-sectional view changed orientation. And if one bot launched a rocket at another from a direction along which your cross-sectional view space was not aligned, the explosion would seemingly come out of nowhere.

But this all assumes that we are using a cross-sectional view space. Why not simply use a more traditional three-dimensional view and then use, say, color to indicate displacement along the fourth dimension? To visualize the concept, imagine an analogous situation in Flatland: A Square is crawling along his two dimensional floor when I fire a rocket at him from above and in front of him. He sees the rocket approaching as if it were in his plane, but it would be tinted bright red. As its vertical displacement decreases, the reddish hue would fade. When it is exactly level with him, it would be a neutral gray, and (assuming I missed), as it passed and continued downward beneath him, would fade to blue.

Of course, if the rocket isn't level with him, it shouldn't obstruct his vision. We would therefore paint it transparently until it crossed his plane. Walls, ceilings, and their fourth-dimensional equivalents could be treated in the same way for a three-dimensional player, and the entire view would be a shifting transparent haze of blue and red walls, players and rockets. It'd be confusing to look at but all the information would be there. Given sufficient time and the adaptability of the human brain (and a key to move ana and kata), I'd bet that a so-inclined player could even learn to play four-dimensional quake.